The present invention relates to the new and distinct cultivar of carnation or pinks from the genus Dianthus and given the cultivar name ‘Appleblossom Burst’. The new plant was the result of an intentional cross on May 14, 2012 under the direction of the inventor between Dianthus ‘WP05 Yves’ U.S. Plant Pat. No. 18,828 as the female or seed parent and ‘Sweetie Pie’ U.S. Plant Pat. No. 27,989 as the male or pollen parent. The cross was harvested and sown in June of 2012. The new hybrid was first selected from trials at a wholesale perennial nursery in Zeeland, Mich. during the summer of 2014 as a single seedling clone and given the breeder code number 13-34-102 later in the evaluation processes. Dianthus ‘Appleblossom Burst’ has been asexually propagated at the same nursery in Zeeland, Mich. since 2014 using traditional shoot tip cutting and shoot tip tissue culture procedures and found to reproduce plants that are identical and exhibit all the characteristics of the original plant.